Can you fly if you have a carotid artery blockage, or is the cabin pressure and altiude too much that it can cause it to dislodge and cause a stroke?

Yes: The primary concern with a carotid blockage is not that the plaque will dislodge, but that the plaque will rupture, causing a blood clot to form on top which can then flow into the brain circulation and cause a stroke. There is no evidence that flying influences this process.

A word of caution: There are no definitive studies on this but strokes make up a significant percentage of in-flight emergencies. It is not that pressure or altitude cause mechanical dislodgement of a piece and then a stroke but the brain living off a vessel with a severe blockage may not be able to accommodate the lower oxygen levels at higher altitude (lack of vascular reserve) and lead to a stroke that way.

Depends : I would suggest discussing this with your neurologist. It likely depends on the size of the carotid blockage and any other flow you may have from other blood vessels. It is probably okay if you have not been operated on yet because if your blockage was really bad you would have had it operated on already.